last year, 2713 teachers attended a technology conference. if there were 163 more men than women at the conference, how many men and how many women attended?
M = W +163
(W+163) + W = 2713
Solve for W, then M.
Let's solve this step-by-step:
Step 1: Let's assume the number of women who attended the conference is x.
Step 2: As given, the number of men is 163 more than the number of women. So the number of men who attended the conference is (x + 163).
Step 3: According to the information given, the total number of teachers who attended the conference is 2713. So, we can set up the equation: x + (x + 163) = 2713.
Step 4: Simplifying the equation, we combine like terms: 2x + 163 = 2713.
Step 5: Subtracting 163 from both sides of the equation gives 2x = 2550.
Step 6: Dividing both sides of the equation by 2, we get x = 1275.
Therefore, 1275 women and (1275 + 163) = 1438 men attended the conference.
To find the number of men and women who attended the technology conference, we can set up a system of equations using the given information.
Let's assume the number of women at the conference is "w".
According to the given information, the number of men attending the conference is 163 more than the number of women. So the number of men is "w + 163".
The total number of attendees is the sum of the number of men and women, which equals 2713: w + (w + 163) = 2713.
Simplifying the equation: 2w + 163 = 2713.
Next, we solve for "w" by isolating the variable:
2w = 2713 - 163
2w = 2550
w = 2550 / 2
w = 1275
Therefore, 1275 women attended the conference.
To find the number of men, we use the equation w + 163:
Number of men = 1275 + 163
Number of men = 1438
Therefore, 1438 men attended the conference.